|
In philosophy and logic, the concept of possible worlds is used to express modal claims, claims that involve notions of possibility or necessity.
For example, the proposition that I am writing this for the Wikipedia can be expressed as: "There is a possible world in which I am writing this for the Wikipedia," which means that the proposition is contingent; that is, it could be otherwise. On the other hand, the proposition "Two plus two equals four" is necessarily true — that is, it is true by definition. This can be expressed as: "There is no possible world in which two plus two does not equal four." Any contingent proposition — any possibility — can be expressed in terms of possible worlds. There is a possible world in which you are not reading this sentence, a possible world in which you do not exist, a possible world in which this sentence will never be written.
The idea of "possible worlds" is most commonly attributed to Gottfried Leibniz, but scholars have also found traces of the idea in the writings of Averroes and John Duns Scotus.
Formal semantics of modal logics
A systematic theory of possible worlds, was first introduced in 20th century work on the semantics of modal logic, led by Saul Kripke. Here possible worlds are used to provide a semantics for claims about possibility and necessity: a statement that is possible is said to be true in at least one possible world; a statement that is necessary is said to be true in all possible worlds, and a statement that is actual is said to be one which is true in the possible world in which we reside.
From formal logic to philosophical tool
From this groundwork, "possible worlds" became a central part of many philosophical arguments in the 1960s and 1970s—including, most famously, the analysis of counterfactual conditionals in terms of "nearby possible worlds" developed by David Lewis and Robert Stalnaker. On this analysis, when we discuss what would have happened if some set of conditions were the case, the truth of our claims is determined by what is true in the nearest possible world (or the set of nearest possible worlds) where the conditions obtain. (A possible world W1 is said to be near to another possible world W2 in respect of R to the degree that the same things happen in W1 and W2 in respect of R; the more different what happens in two possible worlds in a certain respect, the "further" they are from one another in that respect.) To use the example of a counterfactual given earlier, "If George W. Bush hadn't become president of the U.S. in 2000, Al Gore would have.", this sentence would be taken to express a claim that could be reformulated as follows: In all nearest worlds to our actual world (nearest in relevant respects) where George W. Bush didn't become president of the U.S. in 2000, Al Gore became president of the U.S. then instead. And on this interpretation of the sentence, if there is some nearest world to the actual world (nearest in relevant respects) where George W. didn't win but Gore didn't either, then the claim expressed by this counterfactual would be false.
Today, possible worlds play a central role in many debates within philosophy, including especially debates over the Zombie Argument, physicalism and supervenience in the philosophy of mind. Intense debate has also emerged over the ontological status of possible worlds:—provoked especially by David Lewis's defense of modal realism, the doctrine that talk about "possible worlds" is best explained in terms of innumerable, really existing physical worlds other than the one we live in. The question here is: given that modal logic works, and that the possible worlds semantics for modal logic are correct, what has to be true of the world, and what are the "possible worlds" that we range over in our interpretation? Lewis argued that what we range over is nothing more or less than real, physical worlds that can be said to exist in exactly the same way (and to exactly the same degree) as our actual world, but which are distinguished from the actual world by having no spatial or temporal relationship to what happens in it. (On Lewis's account, the only special property that the actual world has is that we are in it.) Others, such as Robert Adams and William Lycan, reject Lewis's picture as metaphysically extravagant, and suggest in its place an interpretation of "possible worlds" as consistent, maximally complete sets of descriptions of or propositions about the world, so that a "possible world" is conceived of as a complete description of a way the world could be—rather than a world which is that way. (Lewis describes their position, and similar positions such as those advocated by Alvin Plantinga and Peter Forrest, as "ersatz modal realism", arguing that such theories try to get the benefits of possible worlds semantics for modal logic "on the cheap", but that they ultimately fail to provide an adequate explanation.) Saul Kripke, in Naming and Necessity, took explicit issue with Lewis's use of "possible worlds" semantics, and defended a stipulative account of possible worlds as purely formal (logical) entities rather than either really existent worlds or as some set of propositions or descriptions.
Comparison with the many-worlds interpretation
The concept of possible worlds has often been compared to the many-worlds interpretation of quantum mechanics; indeed, they are often erroneously conflated. The many-worlds interpretation is an attempt to provide an interpretation of the process of observation leading to the so-called collapse of the wavefunction, the possible-worlds theory is an attempt to provide an interpretation (in the sense of a more or less formal semantics) for modal claims. In the many-worlds interpretation of quantum mechanics, the collapse of the wavefunction is interpreted by introducing a quantum superposition of states of a possibly infinite number of universes.
The main differences between the two notions, aside from their origins and purposes, are:
- The states of quantum-theoretical worlds are entangled quantum mechanically while entanglement for possible worlds may be meaningless;
- depending on the scope of the modal claim, there are possible worlds that are logically but not physically possible.
Suggested Reading
- D.M. Armstrong A World of States of Affairs (1997. Cambridge: Cambridge University Press) ISBN 0-521-58948-7
- John Divers Possible Worlds (2002. London: Routledge) ISBN 0-415-15556-8
- David Lewis On the Plurality of Worlds (1986. Oxford & New York: Basil Blackwell) ISBN 0-631-13994-X
- Michael J. Loux [ed.] The Possible and the Actual (1979. Ithaca & London: Cornell University Press) ISBN 0-8014-9178-9
|
